Theoretical and Mathematical Physics

, Volume 85, Issue 1, pp 1055–1062 | Cite as

Difference analogs of the harmonic oscillator

  • N. M. Atakishiev
  • S. K. Suslov
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    A. Érdelyi et al. (eds), Higher Transcendental Functions (California Institute of Technology H. Bateman M. S. Project) Vol. 2, McGraw Hill, New York (1953).Google Scholar
  2. 2.
    A. F. Nikiforov, S. K. Suslov, and V. B. Uvarov, Classical Orthogonal Polynomials of a Discrete Variable [in Russian], Nauka, Moscow (1985).Google Scholar
  3. 3.
    N. M. Atakishiev and S. K. Suslov, in: Modern Group Analysis: Methods and Applications [in Russian], Élm, Baku (1989), pp. 17–20.Google Scholar
  4. 4.
    I. A. Malkin and V. I. Man'ko, Dynamical Symmetries and Coherent States of Quantum Systems [in Russian], Nauka, Moscow (1979).Google Scholar
  5. 5.
    N. M. Atakishiyev, Lecture Notes in Phys., Vol. 180, Springer-Verlag, Berlin (1983). pp. 393–396; N. M. Atakishiev, Teor. Mat. Fiz.,56, 154 (1983).Google Scholar
  6. 6.
    I. M. Gel'fand, R. A. Minlos, and Z. Ya. Shapiro, Representations of the Rotation and Lorentz Groups and their Applications, Pergamon Press, Oxford (1963).Google Scholar
  7. 7.
    E. Inönü and E. P. Wigner, Proc. Nat. Acad. Sci. USA,39, 510 (1953).Google Scholar
  8. 8.
    W. Miller (Jr.), Symmetry Groups and their Applications, Academic Press, New York (1972).Google Scholar
  9. 9.
    L. D. Landau and E. M. Lifshitz, Quantum Mechanics; Non-Relativistic Theory, 3rd ed., Pergamon Press, Oxford (1977).Google Scholar
  10. 10.
    A. M. Perelomov, Generalized Coherent States and their Applications [in Russian], Nauka, Moscow (1987).Google Scholar
  11. 11.
    A. J. Macfarlane, J. Phys. A,22, 4581 (1989).Google Scholar
  12. 12.
    L. C. Biedenharn, J. Phys. A,22, L873 (1989).Google Scholar
  13. 13.
    L. J. Rogers, Proc. London Math. Soc. (2),25, 318 (1894).Google Scholar
  14. 14.
    L. J. Rogers, Proc. London Math. Soc. (2),16, 315 (1917).Google Scholar
  15. 15.
    G. Szegö, Sitz. Preuss. Akad. Wiss. Phys,-Math. Kl.19, 242 (1926).Google Scholar
  16. 16.
    R. Askey and M. E. H. Ismail, Studies in Pure Mathematics (P. Erdös, ed.), Birkhauser, Boston, Mass. (1983), pp. 55–78.Google Scholar
  17. 17.
    R. Askey and J. A. Wilson, Memoirs Am. Math. Soc., No. 319 (1985).Google Scholar
  18. 18.
    N. M. Atakishiyev and S. K. Suslov, “On the Askey-Wilson polynomials,”, Preprint KMUNTZ 89-04, Leipzig (1989).Google Scholar
  19. 19.
    M. E. H. Ismail, D. Stanton, and G. Viennot, Europ. J. Combinatorics,8, 379 (1987).Google Scholar

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • N. M. Atakishiev
  • S. K. Suslov

There are no affiliations available

Personalised recommendations